The sixth grade first volume mathematics unit 2 knowledge
I. Conditions for determining the position of an object
To determine the position of an object on a plane, we must first determine the observation point, then find the direction and angle (azimuth), and finally determine the distance.
Second, the method of marking the position of the object on the plan:
1, observation point and orientation;
2. Draw a ray from the observation point in a certain direction;
3. Convert the actual distance into the length on the map according to the distance from the ground to the ground indicated by the line segment with unit length;
4. Draw the length of the figure with a ruler and mark the position and name of the observation point.
The conditions for determining the position of an object: direction and distance, both of which are indispensable.
Third, the relativity of positional relationship.
There are two ways to describe the positional relationship between two objects or places, such as "Shanghai is about 30 south-east of Beijing" and "Beijing is about 30 northwest of Shanghai". The angle is the same, but the direction is just the opposite. South by east corresponds to north by west (it can't be said that it is north by west).
Because east, west and north are just the opposite, the relative position of southeast is northwest.
Fourthly, the method of describing the road map
First determine the observation point according to the walking route, and then determine the walking direction and distance. That is, every step should be clear about where to start and how far to go. Every step, change a new observation point.
Verb (abbreviation of verb) method of drawing road map
1, determine the direction and unit length.
2, determine the location of the starting point
According to the description, start from the starting point, find the direction and distance, and draw them one by one. Except for the first paragraph (the starting point is the observation point), the end point of the previous paragraph should be each other's observation points.
4. Who is the observation point and who is the center? Draw a "ten" direction, and then judge the direction and distance of the next point.
Every time you draw a road, you must re-determine the observation point, direction and distance.
Knowledge points of the second unit of sixth grade mathematics in Beijing Normal University
Fractional mixed operation
1, the operation order of decimal mixed operation is exactly the same as that of integer mixed operation, which is multiplication and division first, then addition and subtraction, and bracket operation is bracket operation first.
(1) If the operations are at the same level, the order is from left to right.
(2) If it is a fractional multiplication, the score can be reduced first and then calculated.
(3) If it is a mixed operation of fractional multiplication and division, first convert division into multiplication, and then perform multiplication.
Step 2 solve the problem
(1) Use fractional operation to solve the practical problem of "How many fractions are more (or less) than the known quantity". The method is as follows:
The first method: you can find out more or less specific quantity first, and then add or subtract more or less parts with the unit "1" to find out the required problem.
The second method: you can also add or subtract more or less fractions with the unit "1" to find the fraction of the unknown in the unit "1", and then multiply this fraction with the unit "1".
(2) "Given the sum of A and B, how much does A account for?"
The first method: first, find out who accounts for a fraction of the unit "1", and then subtract the number A from the unit "1" to find the number B.
The second method: subtract the fraction of the sum of known numbers A from the unit "1" to get the fraction of the sum of unknown numbers B, and then calculate the number B. ..
(3) Steps to solve slightly complicated fractional application problems with equations:
① Find the unit "1".
② Determine the relationship between other quantities and the quantity of unit "1", draw the relationship diagram and write the equivalent relationship.
(3) Let the unknown quantity be x, and list the equations according to the equivalence relation.
④ Solve the equation.
(4) Remember the following arithmetic solutions for solving application problems:
① corresponding quantity ÷ corresponding score = quantity in "1"
② Find the fraction of a number and calculate it by multiplication.
③ What fraction of a number is known? Find this number, calculate it by division, and solve it by column equation.
3. Remember the following rules for solving equations:
Appendix+Appendix = Sum
Appendix = Sum-Another Addendum
Negative-negative = difference
Subtraction = difference+subtraction
Subtraction = minuend-difference
Factor × factor = product
Factor = product ÷ another factor
Dividend = quotient
Dividend = quotient × divisor
Divider = Divider
4, the method of drawing a simple line graph
There are two kinds of fractional application problems, one is to find the quantity of unit "1" by multiplication, and the other is to find the quantity of unit "1" by division. The quantitative relations between these two types of application problems can be divided into three types: (1) One quantity is the fraction of the other. (2) How much is one quantity more than the other? (3) One quantity is a few fractions less than the other. When drawing, it is important to deal with the relationship between quantity and quantity, and determine the quantity of the unit "1" in the examination.
Drawing steps:
(1) First, express the unit "1" with a line segment, draw it on it, and draw it with a ruler.
② Divide the unit "1" into several parts evenly, and draw an even division with a ruler. Mark the relevant quantity.
(3) Draw the quantity related to the unit "1" again, according to which of the above three relationships is actually. Mark the relevant quantity.
(4) Questions should be marked with "?" Quantity and unit.
5, add knowledge points
Fractional multiplication: The significance of fractional multiplication is the same as integer multiplication, and it is a simple operation to find the sum of several identical addends.
Calculation rules of fractional multiplication
Fractions are multiplied by integers, and the product of the multiplication of fractions and integers is taken as the numerator, and the denominator remains unchanged; Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator. But the numerator denominator cannot be zero.
Importance of fractional multiplication
Fractional multiplication of integers, like integer multiplication, is a simple operation to find the sum of several identical addends. Multiplying a number by a fraction can be regarded as finding a fraction of this number.
Fractional Multiplying Integer: Combination of Numbers and Shapes, Transformation and Reduction
Reciprocal: Two numbers whose product is 1 are called reciprocal.
Countdown score
Find the reciprocal of the fraction, such as 3/4. Switch 3/4 numerator and denominator, so that the original numerator and denominator are the same. It's four-thirds. 3/4 is the reciprocal of 4/3, or 4/3 is the reciprocal of 3/4.
Reciprocal integer
Find the reciprocal of an integer, such as 12, divide 12 into several components, namely 12/ 1, and then exchange the numerator and denominator of the fraction of 12/ 1 with the original numerator as the denominator. Is112,12 is the reciprocal of112.
Decimal reciprocal
Ordinary algorithm: Find the reciprocal of a decimal, such as 0.25, divide 0.25 into several components, that is, 1/4, and then exchange the numerator and denominator of the fraction of 1/4, with the original numerator as the denominator and the original denominator as the numerator. Then 4/ 1 is calculated by 1: this number can also be divided by 1, for example, 0.25, 1/0.25 equals 4, then the reciprocal of 0.25 is 4, because two numbers whose product is 1 are reciprocal to each other. Fractions and integers also use this law.
Fractional division: Fractional division is the inverse operation of fractional multiplication.
Calculation rules of fractional division:
The number A divided by the number B (except 0) is equal to the reciprocal of the number A multiplied by the number B.
The meaning of fractional division is the same as that of integer division, that is, the product of two factors is known, and one factor is used to find the other factor.
Fractional division application problem: first find the unit 1. Known unit 1. Multiplication is used to find partial quantity or corresponding fraction, and division is used to find unit 1.
Six methods and skills of mathematics
1, get ready:
In the unit preview, we can read roughly, understand the learning content in the recent stage, read carefully in the classroom preview, pay attention to the formation process of knowledge, and record the concepts, formulas and laws that are difficult to understand, so that we can listen to the class with questions.
2. Listen carefully:
Listening to lectures should include listening, thinking and remembering. Listen, listen to the ins and outs of the formation of knowledge, listen to the key and difficult points, and listen to the answers and requirements of examples. Thinking, one is to be good at association, analogy and induction, and the other is to dare to question and ask questions. Taking notes means taking notes in class-methods, doubts, requirements and precautions.
3. Seriously solve the problem:
Classroom exercises are the most timely and direct feedback, and must not be missed. Don't rush to finish your homework, look at your notebook first, review your learning content, deepen your understanding and strengthen your memory.
4, timely error correction:
Classroom exercises, homework, tests and feedback should be consulted in time, the causes of wrong questions should be analyzed, and relevant calculation training should be strengthened when necessary. Ask your classmates and teachers if you don't understand. Don't let the problem hang in the air. Get into the good habit of doing things today.
5, learn to summarize:
"Mathematics and knowledge are closely related. A phased summary can not only play a role in reviewing and consolidating, but also find the connection between knowledge, so as to know fairly well and achieve mastery.
6, learn to manage:
Manage your notebook, exercise book, correction book, and all the exercises and papers you have done. This is the most useful information when reviewing the final exam, and it must not be ignored.
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